The present invention relates to a method of seismic imaging a subsurface formation using a set of seismic sources i and a set of seismic receivers j, wherein there is a complex transmission medium between the two sets. Such a complex transmission medium is for example a complex overburden.
A seismic image of an earth formation is obtained using at least one seismic source and at least one seismic receiver. The source generates a seismic wave into the earth formation, in which formation the seismic wave is reflected by acoustic-impedance contrasts and refracted through media having a variable velocity. The reflected wave is received by the seismic receiver(s). A receiver detects the reflected wave and records it in the form of a signal or seismic trace. The receivers record one signal per receiver and the signals or traces are compiled to yield the seismic image of the underground formation.
Normally, seismic images are obtained with seismic sources and seismic receivers that are located at surface, however, there is a tendency to put the seismic receivers and/or the seismic sources in boreholes, even in horizontal boreholes. However, seismic sources intended for borehole use are typically more expensive than comparable surface seismic sources. Moreover, seismic sources located in a wellbore have the potential to damage the wellbore when activated.
An alternative is to locate the seismic sources at the surface and place the seismic receivers in a borehole. This has the advantage that the receivers can be placed closer to the region of the formation of which an image has to be obtained. This permits the application of a migration algorithm that uses a velocity model of the earth and propagates wave fronts through it. This technique is common and is described in Gray, S. H., et al., Kirchoff Migration Using Eikonal Traveltimes, Geophysics vol. 59, pp. 810-817, Soc. Of Expl. Geophys. 1994. However, this advantage is cancelled if there is a complex transmission medium between the sources and the receivers that distorts the signals. Such a complex transmission medium region is for example a complex overburden.
It will be understood that one way of overcoming this disadvantage is to put the seismic sources in the same borehole. Applicant has now found that it is possible to manipulate the signals in such a way that it appears as if the seismic waves originate from a source at the location of the seismic receiver. Such a source is then called a virtual source, to distinguish it from a real source, which is in this case located at the other side of the complex transmission medium.
To this end the method of seismic imaging a subsurface formation using a set of seismic sources i and a set of seismic receivers j, wherein there is a complex transmission medium between the two sets, which method comprises the steps of
(a) recording with the set of seismic receivers j the signals tij(t) obtained from activating the set of seismic sources i;
(b) selecting a seismic receiver m as the location of a virtual source;
(c) selecting a seismic receiver k, wherein k is in a predetermined range around the position of seismic receiver m;
(d) selecting a seismic source n from the seismic sources i;
(e) time-reversing at least a part of the signal tnm(t) to obtain a time-reversed signal tnm(xe2x88x92t);
(f) convolving the time-reversed signal tnm(xe2x88x92t) with the signal tnk(t) to obtain the convolved signal tconvnmnk(t)=tnm(xe2x88x92t){circle around (xc3x97)}tnk(t);
(g) selecting a next source n, repeating steps (e) and
(f) until a predetermined number of sources have had their turn;
(h) summing the convolved signals over the seismic sources n to obtain a signal                     t                  m          ⁢                      xe2x80x83                    ⁢          k                          v          ⁢                      xe2x80x83                    ⁢          s                    ⁢              (        t        )              =                  ∑        n            ⁢              t                  n          ⁢                      xe2x80x83                    ⁢          m          ⁢                      xe2x80x83                    ⁢          n          ⁢                      xe2x80x83                    ⁢          k                          c          ⁢                      xe2x80x83                    ⁢          o          ⁢                      xe2x80x83                    ⁢          n          ⁢                      xe2x80x83                    ⁢          v                      ,
xe2x80x83where tvsmk(t) is the signal received by a receiver at the position k from a virtual source at the position of receiver m;
(i) repeating steps (c) through (g) over k;
(j) repeating steps (b)-(h) over m to generate a seismic survey with virtual sources m and receivers k; and
(k) further processing the virtual source signals to obtain a seismic image.
In the specification and in the claims the symbol {circle around (xc3x97)} means convolution.